On the Rankin-Selberg problem

被引:57
作者
Huang, Bingrong [1 ,2 ]
机构
[1] Shandong Univ, Data Sci Inst, Jinan 250100, Shandong, Peoples R China
[2] Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China
关键词
SUBCONVEXITY; SUMMATION;
D O I
10.1007/s00208-021-02186-7
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper, we solve the Rankin-Selberg problem. That is, we break the well known Rankin-Selberg's bound on the error term of the second moment of Fourier coefficients of a GL(2) cusp form (both holomorphic and Maass), which remains its record since its birth for more than 80 years. We extend our method to deal with averages of coefficients of L-functions which can be factorized as a product of a degree one and a degree three L-functions.
引用
收藏
页码:1217 / 1251
页数:35
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